Recent history functional linear models for sparse longitudinal data

• Published in: Journal of statistical planning and inference Vol. 141; no. 4; pp. 1554 - 1566
• Main Authors: Kim, Kion, Şentürk, Damla, Li, Runze
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.04.2011; Elsevier
• Subjects: B-splines; Basis expansion; Exact sciences and technology; Functional data analysis; General topics; Global analysis, analysis on manifolds; Linear inference, regression; Local least squares; Mathematics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Smoothing; Sparse design; Statistics; Stochastic processes; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Basis expansion; Sparse design; Local least squares; Smoothing; Functional data analysis; B-splines; B spline; Statistical distribution; Prediction theory; Response model; Stochastic process; Statistical simulation; Linear model; Consistent estimator; Least squares method; Confidence band; Linear estimation; Mathematical expansion; Expansion; Linear functional; Data analysis; Smoothing methods; Prediction; Functional analysis; Statistical estimation; Statistical decision; Statistical method; Response time; Experimental design; Observation data; Filtering theory
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2010.11.003

We consider the recent history functional linear models, relating a longitudinal response to a longitudinal predictor where the predictor process only in a sliding window into the recent past has an effect on the response value at the current time. We propose an estimation procedure for recent history functional linear models that is geared towards sparse longitudinal data, where the observation times across subjects are irregular and the total number of measurements per subject is small. The proposed estimation procedure builds upon recent developments in literature for estimation of functional linear models with sparse data and utilizes connections between the recent history functional linear models and varying coefficient models. We establish uniform consistency of the proposed estimators, propose prediction of the response trajectories and derive their asymptotic distribution leading to asymptotic point-wise confidence bands. We include a real data application and simulation studies to demonstrate the efficacy of the proposed methodology.